Three Statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements. Statements: All pens are newspapers. Some newspapers are novels. No novel is a book. Conclusions: I. Some books are pens. II. Some novels are pens. III. No book is a pen.
Either conclusion I or III follows.
Understanding the Syllogism Statements
We are given three statements and three conclusions. We need to determine which conclusions logically follow from the statements, assuming the statements are true.
The statements are:
- Statement 1: All pens are newspapers.
- Statement 2: Some newspapers are novels.
- Statement 3: No novel is a book.
Let's represent these relationships using symbols or visualize them with Venn diagrams.
- Statement 1 implies that the set of Pens (P) is a subset of the set of Newspapers (N). We can write this as P $\subseteq$ N.
- Statement 2 implies there is an overlap between the set of Newspapers (N) and the set of Novels (V). N $\cap$ V $\neq$ $\emptyset$.
- Statement 3 implies that the set of Novels (V) and the set of Books (B) are mutually exclusive, meaning they have no overlap. V $\cap$ B = $\emptyset$.
Analyzing the Conclusions
Now let's analyze each conclusion based on the given statements.
Conclusion I: Some books are pens.
This conclusion claims there is an overlap between the set of Books (B) and the set of Pens (P). B $\cap$ P $\neq$ $\emptyset$.
From the statements, we know:
- All Pens are Newspapers.
- No Novel is a Book.
- Some Newspapers are Novels.
Since No Novel is a Book, any Newspaper that is also a Novel cannot be a Book. However, the statements don't restrict the relationship between the part of Newspapers that are not Novels and Books. Pens are a subset of Newspapers. So, it is possible that the Pens (which are Newspapers) are located in the part of the Newspaper circle that overlaps with Books (and this part of Newspapers would not overlap with Novels, consistent with statement 3).
For example, suppose there are Newspapers that are not Novels. It is possible some of these Newspapers are Books. Since Pens are just a part of Newspapers, it is possible that some Pens are in this overlap region between Newspapers and Books. Therefore, Conclusion I (Some books are pens) is a possibility.
Conclusion II: Some novels are pens.
This conclusion claims there is an overlap between the set of Novels (V) and the set of Pens (P). V $\cap$ P $\neq$ $\emptyset$.
From the statements, we know:
- All Pens are Newspapers.
- Some Newspapers are Novels.
The statements say Some Newspapers are Novels. Pens are inside Newspapers. The "some newspapers" that are Novels could be the newspapers that are also pens, or they could be newspapers that are *not* pens. The statements do not provide enough information to confirm that the overlap between Newspapers and Novels *must* include Pens.
Consider this possibility: All Pens are Newspapers. The "some newspapers" that are novels happen to be only those newspapers that are *not* pens. In this scenario, no novel would be a pen. Since this scenario is consistent with the statements, Conclusion II does not logically follow from the statements alone.
Conclusion III: No book is a pen.
This conclusion claims there is no overlap between the set of Books (B) and the set of Pens (P). B $\cap$ P = $\emptyset$.
From the statements, we know:
- All Pens are Newspapers.
- No Novel is a Book.
- Some Newspapers are Novels.
As discussed under Conclusion I, the statements allow for the possibility that the Pens (which are Newspapers) are located entirely outside the set of Books. There is no direct statement linking Pens and Books, or linking them indirectly through Novels in a way that forces an overlap or prevents it universally.
Consider this possibility: Pens are inside Newspapers. Novels and Books are separate. The Newspapers that are Novels are separate from Books. The Newspapers that are *not* Novels could potentially contain the Pens, and these Pens could be entirely separate from Books. In this scenario, No Book is a Pen. Therefore, Conclusion III (No book is a pen) is also a possibility.
Checking for Either/Or Case
Let's look at Conclusion I (Some books are pens) and Conclusion III (No book is a pen). These two conclusions form a complementary pair for the relationship between Books and Pens. If "Some books are pens" is true, then "No book is a pen" must be false. If "No book is a pen" is true, then "Some books are pens" must be false.
We found that Conclusion I is possible and Conclusion III is also possible based on the statements. Since these are the only two possibilities for the relationship (either there is some overlap, or there is no overlap), and we cannot definitively prove one to be true while the other is false based solely on the statements, but one of them *must* be true, they form an 'Either/Or' case.
This occurs when a set of statements leads to a situation where a relationship between two terms (here, Books and Pens) is uncertain but must be one of two complementary possibilities (Some are / No are).
Conclusion
Based on the analysis:
- Conclusion I (Some books are pens) is possible.
- Conclusion II (Some novels are pens) does not logically follow.
- Conclusion III (No book is a pen) is possible.
- Conclusions I and III form an 'Either/Or' pair because one must be true, and the other must be false, but the statements do not confirm exactly which one is true.
Therefore, either conclusion I or conclusion III follows logically from the statements.
Revision Table: Syllogism Statement Types
| Type | Statement Structure | Relationship Implied |
|---|---|---|
| A | All X are Y | X $\subseteq$ Y (X is a subset of Y) |
| E | No X is Y | X $\cap$ Y = $\emptyset$ (X and Y are disjoint) |
| I | Some X are Y | X $\cap$ Y $\neq$ $\emptyset$ (X and Y overlap) |
| O | Some X are not Y | Part of X is outside Y |
Additional Information: Introduction to Syllogism
A syllogism is a type of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions (statements) that are assumed to be true. In a categorical syllogism, the statements relate categories (like 'pens', 'newspapers', 'novels', 'books'). The structure typically involves two premises and a conclusion, connecting three terms (a major term, a minor term, and a middle term). Validity in syllogism refers to whether the conclusion logically follows from the premises, regardless of whether the statements are factually true in the real world.
The problem above is a classic example of testing logical deduction skills based on provided statements and conclusions.
Similar Questions
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follows from the statements.
Statements:
All lemons are plums.
All plums are dates.
Some dates are mangoes.
Conclusions:
I. Some lemons are mangoes.
II. Some mangoes are plums.
III. All lemons are dates.
IV. Some mangoes are dates.
Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
Some cards are postcards.
Some cards are envelopes.
All envelopes are copies.
Conclusions:
I. Some copies are envelopes.
II. Some postcards are copies.
III. Some cards are copies.
Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some spices are medicines.
All medicines are chemicals.
No chemical is cheap.
Conclusions:
I. Some medicines are cheap.
II. Some chemicals are spices.
III. No medicine is cheap.
In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements.
Statements:
I. No streak is a line.
II. Some lines are bands.
III. All bands are flashes.
Conclusions:
I. Some flashes are streaks.
II. No flash is a line.
Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
All oranges are apples.
Some oranges are bananas.
All bananas are fruits.
Conclusions:
I. Some fruits are apples.
II. Some apples are bananas.
III. Some oranges are fruits.
Select the Venn diagram that best illustrates the relationship between the following classes.
Swimming, Running, Sports
Select the Venn diagram that best illustrates the relationship between the following classes.
Dialect, Language, Communication
Three statements are given followed by three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements:
Some seeds are fruits.
Some fruits are jams.
All jams are desserts.
Conclusions:
I. Some jams are seeds.
II. Some desserts are jams.
III. Some fruits are desserts.
Three Statements are given followed by Three conclusions numbered I, II and III. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.
Statements :
All stars are moons.
Some moons are suns.
All suns are satellites.
Conclusions :
I. Some satellites are moons.
II. Some satellites are stars.
III. Some moons are stars.
Three statements are followed by three conclusions numbered I, II and III. You have to consider these statements to be true, even if they seem to be at variance with commonly known facts. Decide which of the given conclusions logically follow(s) from the given statements.
Statements:
All tools are spanners.
Some spanners are utensils.
No spanner is an iron.
Conclusions:
(I) Some tools are irons.
(II) Some utensils are tools.
(III) Some utensils are not iron.
Important Questions from Syllogism
The statements below are followed by conclusions labeled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All twenty are thirty.
All thirty are forty.
All forty are sixty.
All sixty are seventy.
Conclusions:
I. Some forty are thirty.
II. Some seventy are sixty.
III. No thirty is twenty.The statements below are followed by two conclusions labelled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.
Statements:
All Strong are animals.
Some animals are Tigers.
All Tigers are Sharp.
Conclusions:
I. Some Strong are Sharp.
II. No Strong is Sharp.The statements below are followed by conclusions labelled I, II and III. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some women are weak.
Some weaks are female.
All female are iron.
All iron are gold.Conclusions:
I. Some weaks are iron.
II. Some gold are weaks.
III. Some women are female.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally established facts, decide which conclusion(s) logically and definitely follow(s) from the information given in the statements.Statements:
Some teaspoons are glasses.
All teddies are teaspoons.
Conclusions:
I. Some teddies are glasses.
II. Some glasses are teddies.
The statements below are followed by two conclusions labeled I and II. Assuming that the information in the statements is true, even if it appears to be at variance with generally Established facts, decide which conclusion(s) logically and definitely follow(s) from the Information, Given in the Statements.
Statements:
All bangles are rings.
Some rings are toys.
Some toys are dolls.
Conclusions:
I. Some rings are bangles.
II. Some dolls are rings.
